philosopher, was a child prodigy. At the age of 12, he proved
Euclid's 32nd theorem that the sum of the angles of a triangle is
equal to two right angles. Before age 16, he wrote a book on conic
sections. He is famous for his theorem that a hexagon inscribed in
a conic section has the property that the three meeting points of
the opposed sides are always in a straight line. He constructed a
calculator, which could handle nine-digit numbers, in 1644 to
assist his father, also a gifted mathematician, in tax
computations he did as a local government official. He had
Torricelli's mercury barometer carried up a mountain and found
that the height of the column dropped as altitude increased, and
thus that air pressure decreased with altitude. This showed that
the attribution of these effects to nature's abhorrence of a
vacuum were due instead solely to the weight and pressure of air.
He determined that the height to which the mercury rose was the
same regardless of the shape of the vessel containing it. Around
1646, he did experiments with double vacuums and on the results
formulated his principle that pressure applied to a confined
liquid is transmitted undiminished through the liquid in all
directions regardless of the area to which the pressure is
applied. Around 1653, he laid the foundations for the theory of
probabilities after being asked by a gambling friend why, in
playing dice, some frequencies came up more often than others. He
developed a means of calculating probabilities with his "Pascal's
Triangle" of coefficients of (a+b) raised to the nth power. Each
row represents the coefficients of a power one greater than the
power of the previous row. Each number is the sum of the nearest
two numbers in the row above it.
Jean Ray from France concluded from his experiments that every
piece of material has a given weight, including air and fire. Otto
von Guericke from Germany discovered that, in a vacuum, sound
does not travel, fire is extinguished, and animals stop breathing.
At a time when mathematics was only a business of traders,
merchants, seamen, carpenters, and surveyors, mathematician John
Wallis, the son of a minister, studied sections of cones [circles,
ellipses, parabola, and hyperbolas] as curves of the second
algebraic degree, i.e. with an exponent of two, i.e. y =
(a (x squared)) + b. He also worked with negative and fractional
exponents. Around 1655 he invented the infinite arithmetic and
introduced the symbol for infinity. He determined that the area
under any curve defined by the equation y = (x to the nth power),
was x to the (n+1)th power divided by n+1. He introduced the
concept of the limit of a string of numbers. He wrote a treatise
on algebra which was historical as well as practical. He also
decoded enemy cyphers for the sovereign.
Some English gentlemen interested in the new scientific methods
originated by Galileo had meetings beginning about 1645 to discuss
scientific topics. One group met at Gresham College and was headed
by Wallis. Another group was led by Robert Boyle, a philosopher,
physicist, and chemist. They wrote in English instead of Latin.
These meetings later gave rise to the Royal Society for science.
The Merchant Adventurers were incorporated again in 1643 to have a
monopoly. It was required to admit into membership for 100 pounds
anyone free of London and bred as a merchant, and for 50 pounds
any non-inhabitant of London. The penalty for trading for one who
was not free of the corporation was forfeiture of his goods.
In 1648, the House of Commons abolished the monarchy and in 1649
the House of Lords. Also in 1649 it declared that England "should
thenceforth be governed as a commonwealth and free state by the
supreme authority of this nation, the representatives of the
people in Parliament." It made a new constitution.
John Milton defended the Commonwealth as superior to the monarchy
because it could not deteriorate into tyranny in his books: "First
Defense of the People of England" in 1651, and "Second Defense" in
1654. He lauded Cromwell as great in war and great in peace, and
exemplifying the principle that "nature appoints that wise men
should govern fools".
Thomas Hobbes, the son of a clergyman, and tutor to students,
wrote "Leviathan" in 1651 on his theory of sovereignty. Hobbes
thought that states are formed as the only alternative to anarchy,
barbarism, and war, so that supremacy and unity of a sovereign
power is essential to a civilized life and the protection of the
citizenry. A sovereign may be a man or body of men as long as his
or its authority is generally recognized. There must be a social
contract among the citizenry to obey a certain sovereign. To avoid
religious conflict, there must be a complete subordination of the
church to the state and the religion of a state must be dependent
upon its secular sovereign. Hobbes thought that knowledge of the
world came through experience and not reason alone. Only matter
exists, and everything that happens can be predicted in accordance
with exact, scientific laws. He regarded human societies as purely
mechanical systems set in motion by human desires. He saw self
interest as the mainspring of moral law. Conflicting self
interests transformed into a lawful system of agreements. Hobbes
opined that all power really originated in the people and that the
end of all power was for the people's good.
On the other hand, James Harrington, who wrote "The Commonwealth
of Oceana" in 1656, opined that a stable society depended on a
direct relationship between the distribution of property and
political power; no one with property worth more than 2,000 pounds
should be allowed to acquire more and property should be divided
among children. A senate of mature property owners were to make
and debate the laws while an assembly elected by universal
suffrage was to vote on them because "a popular assembly without a
senate cannot be wise and a senate without a popular assembly will
not be honest". A third of the Senate would turn over every year.
John Milton defended the execution of the King in "The Tenure of
Kings and Magistrates" in which he maintained that the people may
"as often as they shall judge it for the best either to choose
him or reject him or depose him, though no tyrant, merely by the
liberty and right of freeborn men to be governed as seems to the
best". He also wrote in favor of liberty of the press. Ordinary
speech found its way into prose writing.
Lands of more than 700 Royalists, including church lands, were
confiscated and sold or leased by county committees. Many
Royalists put their lands into trusts or turned them over to
relatives or sold them outright to prevent confiscation. It was an
upheaval comparable to the dissolution of the monasteries. Also,
specified Papists who had taken up arms against the realm lost
their lands, goods, money, rents, and two-thirds of their
personal estates. But allowance was made for the maintenance of
their wives and children.
The Book of Common Prayer was abolished because of its burdensome
ceremonies. It was replaced by a Directory for Public Worship.
According to this, the Sunday service was to include reading of
the Scriptures, prayer, and a sermon, ordinarily on some text of
scripture which would be explained with reasons therefore and
applied to peoples' lives so they could see it they had sinned or
not. The ending of episcopal patronage gave some parishes the
right to elect their own ministers.
All festivals and holy days were abolished, e.g. Christmas,
Easter, Whitsuntide. Instead, scholars, apprentices, and servants
were to have recreation and stores were to be closed every second
Tuesday of the month. The usual merry-making, music, dancing, and
sports after the Sunday service were discontinued.
A day for fasting: the last Wednesday of every month, was declared
by statute. This day was to be "kept with the more solemn
humiliation, because it may call to remembrance our sins, and the
sins of our forefathers, who have turned this Feast, pretending
the memory of Christ into an extreme forgetfulness of him, by
giving liberty to carnal and sensual delights, being contrary to
the life which Christ himself led here upon earth, ...". This
statute lasted for only five years from 1644 because observance of
it was not consistent throughout the country.
Educational opportunities such as in grammar schools were more
widespread and stronger than ever before or since until the 1800s.
About 78% of men in London were literate, and 30% of men
nationwide. About half the women in London were literate by 1700.
In 1645, the marshalls of the admiralty and five major ports were
ordered to search all ships for stolen children since it had been
a problem in London.
The elderships of the church were given power in 1645 to suspend
from the sacrament of the Lord's Supper all ignorant and
scandalous persons. Ignorance was lack of knowledge that there is
a God and this is the one true God we worship, that this God is
one, yet three persons" Father, Son, and Holy Ghost, that God
created man in his own image, that all have sinned and therefore
shall die, that there is one mediator between God and man: Jesus
Christ, who died on the cross to save men from their sins, that he
rose from the dead, ascended into heaven, sits at the right hand
of God, and intercedes for us, that Christ and his benefits are
applied only by faith, that the souls of the faithful live with
Christ in blessedness, that non-believers and non-repenters shall
perish eternally, that the sacraments are baptism and communion,
and that there is a judgment day on which the righteous will be
given life eternal and the wicked shall receive everlasting
punishment. Scandalous persons are those who blasphemously speak
or write anything of God, his holy work or the sacraments; an
incestuous person; an adulterer; a fornicator; a drunkard; a
profane swearer or cursor; a murderer; a worshipper of images,
crosses, crucifixes, relics, saints, or angels; makers of images
of the trinity; one who professes not to be in charity with his
neighbor; any challenging another to fight or accepting such
challenge; on the Lord's day, dancing, dicing, cards, masking,
wake, shooting, bowling, football, wrestling, plays, interludes,
fencing, bullbaiting, bearbaiting, hawking, hunting, coursing,
fishing, fowling, selling wares, travel without reasonable cause;
a brothel-house keeper; one who solicits the chastity of another;
one who marries a Papist or consents to the marriage of his child
to a Papist; own who goes for advice to a witch, wizard, or
fortune-teller; one who assaults his parents, or any magistrate,
minister, or elder in the execution of his office; and one
attainted of barratry, forgery, extortion, or bribery. If such a
person persists, he shall be excommunicated.
Cromwell did not disapprove of activities prohibited because of
the recreation they provided, but thought that they had become too
central to people's lives. He did not close the taverns or ale
houses.
In 1653 it was required that public preachers be approved by a
commission nominated by the Lord Protector and Parliament because
there had been too many "weak, scandalous, popish, and ill-
affected" ones. In 1654 named persons were ejected as scandalous,
ignorant and insufficient ministers and schoolmasters.
In 1649 a corporation was established to teach the Gospel of Jesus
Christ in New England to Indians.
Because the poorer parishes of London were having problems
supporting their poor, a Corporation for the poor of London was
established in 1647 with authority to erect workhouses and houses
of correction.
Imprisoned debtors who had less than five pounds and less that
five pounds worth of trade tools and clothing and bedding for his
family were ordered released in 1649.
Wardship was abolished. Military tenures were abolished. Feudal
tenures were converted into freehold in 1646.
In 1653 those living in Crown forest land were given free socage
in that land. The game laws were not enforced, so people could eat
deer.
Enclosures were increasing and Parliament was disinclined to
protect copyholders against enclosures, favoring those with rights
of ownership. Enclosure was no longer deterred especially after
abolition of the Star Chamber. The legal device of "strict
settlement" evolved to prevent heirs from breaking up estates
enabled families to concentrate land and capital into large units.
The oldest son inherited the land and the younger sons now
received money. Clover seed was sold in London by 1650. It
revolutionized the cultivation of barren land. England began to
export instead of import grain. But vagrancy increased from people
dispossessed of land. And the village artisan, when deprived of
his field and of this rights of common, could not continue to work
at home, but had to accept the wages offered to him in an
employer's workshop.
Employers and entrepreneurs were now free from control by the
Crown. There were no more attempts to supervise quality of
manufactures or to fix prices or regulate wages. There was greater
freedom established in relations between employers and workers.
The government no longer tried to compel employers to keep
employees in times of economic slump. The requirement of seven
year apprenticeships and being the son of a freeholder to be an
apprentice were not enforced.
The economy was still volatile due ostensibly to variable
harvests, amount of gold and money in circulation, and balances of
trade, and to periods of plague. Wages rose steadily. The rise in
prices ended about 1650, and prices remained stable until about
1775. There was more mobility of people. Taxation became regular
and it was controlled by representatives of the taxpayers.
Population growth gradually stabilized.
Capitalism was coming into being. For instance, the clothier was
now a manufacturer. He had become a contractor, taking wool to the
specialist spinner, the yarn to the specialist weaver, the rough
cloth to be washed and stretched, and finally to the dyer. This
cloth was sold at retail by the drapers. Tin on the surface was
exhausted, so capital was used to drive deep shafts in tin mines.
No longer did a single man with a single ship sail around until he
found a market, but company trading overseas had their ships,
wharves, and depots furnished by men's savings put into a common
stock. The first major capitalist industries were coal mining,
iron mining, and foreign trade because they all needed large
investments, and thus joint-stock company organization.
Cromwell reconstituted the East India Company on a wider and more
permanent basis. He gave it a new charter in 1657 which included
authority to make stock permanent, thus ensuring a continuity of
capital. This solved the problem of the competition of overlapping
voyages which still occurred despite their terms of several years.
The company became one of the first permanent joint-stock
companies. Now the stock was never wound up. The Company had
permanent capital which could grow. The absence of competition
among voyages made the Company stronger in the face of a common
enemy, such as a rival trading country or Indian groups. The
charter also authorized the company to fortify and colonize any of
its establishments and to transport to them settlers, stores, and
ammunition.
Later in 1657, the Company threw open the freedom of the Company
to the public for a nominal sum of five pounds. Now the Merchant
Adventurers and private traders could participate. It provided
that dividends were to be paid only in cash and not in kind
(goods). It also provided for appraisals of the Company's property
to be made every three years, so any shareholders could redeem
their shares proportionately. His shares would then be resold.
People began to buy and sell their shares among each other. The
Company made the minimum subscription 100 pounds. Each person
holding 500 pounds worth of shares had one vote. Holding 1,000
pounds worth of shares qualified one for election to the committee
of twenty-four. The seats of the members of this committee and of
the Governor and Deputy Governor could no longer be permanent, but
had limited and staggered terms. The continuity of capital took
the place of the permanence of the governing body in providing
stability. There was a regular scale of salaries for employees,
and rules of conduct such as the one disallowing any clerk of the
India House from going to play houses, dancing schools, or
taverns. The Company established almshouses for its widows and
orphans.
In 1657 the Muscovy Company, renewed its charter for trade in
Russia and established a New General Stock. If a man bought a
share, he bought freedom of the company. An annual dividend was
declared from the annual profits.
Commercial men regularly kept accounts with bankers. Merchants
used division to apportion profits or losses to the parties whose
capital was involved. Simple and compound interest were used. The
concept of contract became a familiar one.
Regular private bankers of London emerged from the Goldsmiths from
1640 to 1675. They issued bank notes and paid checks.
Cromwell increased trade by seizing territories, establishing
colonies, and warring with competitors for master of the seas and
trade. In 1649 it was provided that no one who paid his assessment
for soldiers' pay would have to quarter any of them.
Authority was given in 1649 to impress seamen: mariners, sailors,
watermen, surgeons, gunners, ship carpenters, caukers, coopers,
whoymen, and carmen for carriage of victuals.
English ships were embellished with decoration. Their sail area
was increased by triangular fore and aft sails. The Navy increased
from 39 to 80 vessels.
After serving in foreign wars, ex-soldiers were allowed in 1654 to
practice any trade without serving a seven year apprenticeship.
Colonies New Hampshire and Maine were established in 1635,
Connecticut in 1636, and Rhode Island in 1638, as offshoots from
other colonies.
About 1650, steel was hardened by repeated quenchings and
temperings when the steel had reached certain colors. Brass was
made from copper and zinc alloyed together.
There were power-driven rolls for the coinage from 1657. Strips of
silver were passed between engraved rolls. Then coins were punched
out and their edges serrated.
In the 1650s, Huygens made the first pendulum that worked
practically in a mechanical clock. This new clock increased the
accuracy of time-keeping tenfold. He also introduced the concept
of mathematical expectation into probability theory.
There was a thermometer which used liquid such as water or alcohol
in a glass tube instead of air.
Dutchman Stevinus showed that the pressure at the bottom of a
column of liquid is proportional to the height of the column, and
not to its bulk, about 1634. He also studied oblique forces, and
the balancing of such that could bring about "stable equilibrium".
Blaise Pascal, a French mathematician, physicist, and religious
philosopher, constructed a calculator in 1644 to assist his
father, who was involved in local administration, in tax
computations. Around 1646, he proved his law that pressure applied
to a confined liquid is transmitted undiminished through the
liquid in all directions regardless of the area to which the
pressure is applied. Around 1653, he laid the foundations for the
theory of probabilities, including the creation of "Pascal's
Triangle" of coefficients of (a=b) raised to the nth power. He and
lawyer and mathematician Pierre Fermat invented the theory of
probabilities.
Fermat also proved that the law for refraction (bending) of light
results from light's following the path that takes the shortest
time. He founded number theory, the study of properties of whole
numbers, in 1640. Fermat formulated the notion of a line tangent
to a curve and started the development of differential calculus,
in which a rate of change is expressed as a function of time in
equation form and also as a tangent to the curve associated with
that equation. This work helped lay the foundation for analysis.
He and German Gottfried Leibniz formulated the principle that an
equation with two unknown quantities can represent a curve.
Leibnitz believed that man's mind can arrive at truths about
entities by pure thought.
Since the Puritans forbade music in churches, but enjoyed it in
domestic circumstances, much secular music was composed,
published, and played. There were many musical clubs. The violin
became very popular. Solo songs were much sung. The first English
opera: "The Siege of Rhodes" was written and performed with women
on stage. Writers of the time included John Milton, political
philosopher James Harrington, poet Edmund Waller, Thomas Fuller,
poet Abraham Cowley, and biographer Issak Walton. John Aubrey
wrote anecdotes about famous men. Jeremy Taylor, chaplain to
Charles I, wrote on theology. People still read French romances
translated into English. Dancing was still popular. Coffee houses
came into prominence as places of social discourse. The first
coffee house was established in London in 1652; ten years later,
there were 82 coffee houses in the City. There were elegant
pleasure gardens, with a fee for access. They were used for
promenades and picnics. Ladies and their gallants rendezvoused
there. Cromwell introduced the habit of port drinking to England.
In 1657, one general Post Offices was established with one
Postmaster General for all of England. No other person could have
the horsing of the through-posts. It cost 2d. for a letter to or
from 80 miles of London and 3d. for one outside 80 miles of
London.
There was continual problem with Catholics. Mayors, Justices and
capital burgesses of towns where Papists or others had caused
rebellion and insurrection and plundered, robbed, pillaged,
murdered and raped, were given the power in 1642 to call,
assemble, train, and arm soldiers for defense. The Committee of
the Militia of London was given authority in 1647 to search all
houses and places for Papists and to search for and seize any
arms, ammunition, and war materials in custody of such persons. In
1648, all Papists and soldiers of fortune who had borne arms
against Parliament were ordered to depart from within twenty miles
of London and Westminster or be imprisoned as traitors. In 1657
convicted Papists and people marrying convicted Papists were
required to take an oath renouncing the pope and Catholic Church
or lose two-thirds of their lands and estate, retaining their
house on the remaining one-third. If one went to mass in an
ambassador's house, the fine was 100 pounds and imprisonment for
six months, one half going to the informer. In 1659 all
householders in London and Westminster had to give a list of
persons lodging in their house, and the horses and arms there. But
the laws against Catholics practicing their religion were not
rigorously enforced, nor were those against adherents of the
formerly established Church of England.